网络流最大流 Edmonds-Karp算法

最新推荐文章于 2024-02-07 08:43:41 发布

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最新推荐文章于 2024-02-07 08:43:41 发布

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分类专栏： [Graph Theory]

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本文介绍了一个基于Edmonds-Karp算法实现的最大流问题解决方案，并通过C++代码详细展示了如何构造网络图并求解从指定起点到终点的最大流量。

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#include <iostream>
#include <queue>
#include <climits>
#include <cstring>
using namespace std;

const int MAX_SIZE = 100;

int capacity[MAX_SIZE][MAX_SIZE];
int parent[MAX_SIZE];
bool visit[MAX_SIZE];

int vertex_num;
int edge_num;


void init(){
    
    memset( visit, false, sizeof( visit ) );
    
    cout << "Enter vertex_num and edge_num : ";
    cin >> vertex_num >> edge_num;
    
    for( int i = 1; i <= edge_num; ++i ){
        
        int u, v, cap;
        
        cout<<"Enter u and v and capacity : ";
        cin >> u >> v >> cap;
        capacity[u][v] = cap;
        
    }

}


bool Edmonds_Karp( int start, int end ){
    
    queue< int > Q;
    memset( visit, false, sizeof( visit ) );
    
    visit[start] = true;
    Q.push( start );
    
    while( !Q.empty() ){
        
        int temp = Q.front();
        Q.pop();
        
        for( int i = 1; i <= vertex_num; ++i ){            
            if( capacity[temp][i] && !visit[i] ){                
                visit[i]  = true;
                parent[i] = temp;
                Q.push( i );
                
                if( i == end ) 
                    return true;                    

            }            
        }
        
    }
    
    return false;

}


int Ford_Fulkerson( int start, int end ){
    
    int max_flow = 0;
    
    while( true ){
        
        if( !Edmonds_Karp( start, end ) ) 
            break;
            
        int flow = INT_MAX;
        int path = end;
        
        while( path != start ){            
            flow = min( flow, capacity[parent[path]][path] );
            path = parent[path];            
        }
        
        path = end;
        
        while( path != start ){            
            capacity[path][parent[path]] += flow;
            capacity[parent[path]][path] -= flow;
            path = parent[path];            
        }
        
        max_flow += flow;
    }
    
    return max_flow;

}


int main(){
    
    init();
    
    int start, end, max_flow;
    
    cout << "Enter start point and end point: ";
    cin >> start >> end;
    
    max_flow = Ford_Fulkerson( start, end );
    cout << "Max Flow : " << max_flow << endl;
    
    return 0;

}